FIA NLS Models: Biomass vs. Stand Age, G-Reconciled
JAH
2023-04-26
Background
This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): biomass productivity trend, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selects the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).
model 1: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
model 2: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)
sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)
sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)
Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Two Log-normal models are fitted: 1) the simple model, and 2) the \(\alpha\) model: account for growth compensation due to plot biomass loss.
model 4: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
model 5: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval
This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6880 1758.3
## 2 6827 1549.6 53 208.71 17.349 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 74579.98
## 2 2 73289.04##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.67452 0.17477 3.86 0.000115 ***
## alpha 0.84798 0.02771 30.60 < 2e-16 ***
## A 393.99644 24.36456 16.17 < 2e-16 ***
## k 172.58285 11.68008 14.78 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4764 on 6827 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.999e-06
## (53 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6827 1549.6
## 2 6826 1548.9 1 0.76688 3.3797 0.06605 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 73289.04
## 2 2a 73287.66
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 6.980e-01 1.765e-01 3.954 7.78e-05 ***
## alpha 8.460e-01 2.759e-02 30.667 < 2e-16 ***
## A 4.393e+02 4.894e+01 8.977 < 2e-16 ***
## k 2.106e+02 3.476e+01 6.058 1.46e-09 ***
## p 9.141e-03 4.824e-03 1.895 0.0581 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4763 on 6826 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 8.999e-06
## (53 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6878 1726.3
## 2 6825 1505.9 53 220.44 18.851 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 73287.66
## 2 3 74457.48
## 3 4 73097.37##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.88132 0.18708 4.711 2.52e-06 ***
## alpha 0.84265 0.02664 31.627 < 2e-16 ***
## a 37.96496 1.70575 22.257 < 2e-16 ***
## b 102.86051 4.64467 22.146 < 2e-16 ***
## c 114.69627 4.21714 27.198 < 2e-16 ***
## d 0.92535 0.03937 23.504 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4697 on 6825 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (53 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 22648 8866.6
## 2 18856 6793.7 3792 2072.9 1.5173 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 236627.9
## 2 2 196558.7##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.36931 0.11282 3.273 0.00106 **
## alpha 0.70673 0.02261 31.251 < 2e-16 ***
## A 170.68000 4.81077 35.479 < 2e-16 ***
## k 63.81081 1.90831 33.438 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6002 on 18856 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 6.72e-06
## (3825 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18856 6793.7
## 2 18855 6696.2 1 97.51 274.57 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 196558.7
## 2 2a 196288.1
## 3 2b 196519.3
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.120e-01 1.094e-01 2.853 0.00434 **
## alpha 7.206e-01 1.903e-02 37.868 < 2e-16 ***
## A 2.250e+02 1.037e+01 21.689 < 2e-16 ***
## k 1.207e+02 8.513e+00 14.184 < 2e-16 ***
## p 4.607e-02 2.146e-03 21.469 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5959 on 18855 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 7.664e-06
## (3825 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 22646 8719.0
## 2 18854 6480.3 3792 2238.6 1.7176 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 196288.1
## 2 3 236251.5
## 3 4 195672.2##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.50006 0.11585 4.317 1.59e-05 ***
## alpha 0.78377 0.01478 53.030 < 2e-16 ***
## a 23.58921 0.68133 34.622 < 2e-16 ***
## b 78.95623 2.10236 37.556 < 2e-16 ***
## c 109.35069 2.95706 36.979 < 2e-16 ***
## d 1.19460 0.02909 41.065 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5863 on 18854 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3825 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7303 1344.5
## 2 7237 1180.5 66 163.99 15.232 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 79950.98
## 2 2 78502.49##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.12684 0.11521 1.101 0.271
## alpha 0.82089 0.02646 31.029 <2e-16 ***
## A 489.30464 25.34219 19.308 <2e-16 ***
## k 148.21326 8.79104 16.860 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4039 on 7237 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.733e-06
## (66 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7237 1180.5
## 2 7236 1180.4 1 0.066948 0.4104 0.5218
## model AIC
## 1 2 78502.49
## 2 2a 78504.07
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.12684 0.11521 1.101 0.271
## alpha 0.82089 0.02646 31.029 <2e-16 ***
## A 489.30464 25.34219 19.308 <2e-16 ***
## k 148.21326 8.79104 16.860 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4039 on 7237 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.733e-06
## (66 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7301 1330.8
## 2 7235 1163.2 66 167.61 15.796 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 78502.49
## 2 3 79879.95
## 3 4 78399.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.18210 0.11745 1.55 0.121
## alpha 0.82346 0.02507 32.84 <2e-16 ***
## a 30.30540 2.04883 14.79 <2e-16 ***
## b 165.27194 7.48047 22.09 <2e-16 ***
## c 136.54936 9.18585 14.87 <2e-16 ***
## d 1.34424 0.06314 21.29 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.401 on 7235 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (66 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5841 1995.4
## 2 4838 1497.5 1003 497.98 1.6041 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 62741.48
## 2 2 51878.97##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.14016 0.19526 0.718 0.473
## alpha 0.83989 0.04203 19.982 <2e-16 ***
## A 419.45906 34.98507 11.990 <2e-16 ***
## k 179.10235 16.49883 10.855 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5563 on 4838 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.159e-06
## (1004 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4838 1497.5
## 2 4837 1497.4 1 0.059639 0.1927 0.6607
## model AIC
## 1 2 51878.97
## 2 2a 51880.78
## 3 2b 51860.89
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.20453 0.20079 1.019 0.308
## alpha 0.86125 0.04247 20.280 < 2e-16 ***
## A 245.89228 25.01931 9.828 < 2e-16 ***
## k 74.26959 10.35307 7.174 8.41e-13 ***
## s 1.25896 0.06043 20.833 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5552 on 4837 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.132e-06
## (1004 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5839 1955.8
## 2 4836 1444.1 1003 511.72 1.7085 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 51860.89
## 2 3 62628.31
## 3 4 51707.33##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.21911 0.19834 1.105 0.269
## alpha 0.86098 0.03492 24.656 <2e-16 ***
## a 25.85799 1.56357 16.538 <2e-16 ***
## b 113.29766 5.56958 20.342 <2e-16 ***
## c 102.72706 4.47856 22.938 <2e-16 ***
## d 1.02269 0.04585 22.304 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5465 on 4836 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1004 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9996 1894.8
## 2 8721 1571.7 1275 323.07 1.406 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 104296.40
## 2 2 90861.83##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.09397 0.10097 0.931 0.352
## alpha 0.75907 0.02717 27.941 <2e-16 ***
## A 246.44415 8.71838 28.267 <2e-16 ***
## k 71.27405 3.32328 21.447 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4245 on 8721 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.84e-06
## (1281 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8721 1571.7
## 2 8720 1571.5 1 0.17079 0.9477 0.3303
## model AIC
## 1 2 90861.83
## 2 2a 90862.88
## 3 2b 90829.10
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.11062 0.10156 1.089 0.276
## alpha 0.76461 0.02731 27.993 <2e-16 ***
## A 180.02124 8.11605 22.181 <2e-16 ***
## k 39.98216 2.53118 15.796 <2e-16 ***
## s 1.35814 0.06011 22.594 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4237 on 8720 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.045e-06
## (1281 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9994 1868.9
## 2 8719 1536.5 1275 332.39 1.4794 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 90829.10
## 2 3 104162.96
## 3 4 90668.25## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "223", , value =
## structure(list(: provided 32 variables to replace 31 variables##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.11966 0.10084 1.187 0.235
## alpha 0.76968 0.02605 29.541 <2e-16 ***
## a 31.40344 1.93795 16.204 <2e-16 ***
## b 103.16970 3.44725 29.928 <2e-16 ***
## c 102.24785 4.00685 25.518 <2e-16 ***
## d 1.21271 0.05204 23.301 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4198 on 8719 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1281 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12796 4809.1
## 2 12522 4175.6 274 633.55 6.9341 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 141420.6
## 2 2 137621.6##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.25689 0.14587 8.617 <2e-16 ***
## alpha 0.58948 0.01827 32.263 <2e-16 ***
## A 219.72489 7.22935 30.393 <2e-16 ***
## k 48.95756 1.56970 31.189 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5775 on 12522 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.264e-06
## (318 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12522 4175.6
## 2 12521 3965.0 1 210.56 664.91 < 2.2e-16 ***
## 3 12520 3860.0 1 104.98 340.50 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 137621.6
## 2 2a 136975.5
## 3 2b NA
## 4 2c 136641.4##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.160e+00 1.852e-01 11.66 <2e-16 ***
## alpha 8.060e-01 1.026e-02 78.53 <2e-16 ***
## A 1.278e+02 4.542e+00 28.14 <2e-16 ***
## k 3.209e+01 8.753e-01 36.66 <2e-16 ***
## p 2.013e-01 7.285e-03 27.63 <2e-16 ***
## s 2.406e+00 1.056e-01 22.79 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5553 on 12520 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 9.748e-06
## (318 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12794 4770.2
## 2 12520 3858.0 274 912.2 10.804 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 136641.4
## 2 3 141320.7
## 3 4 136634.9##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.12172 0.18310 11.59 <2e-16 ***
## alpha 0.80660 0.01021 79.02 <2e-16 ***
## a 26.09875 0.76750 34.01 <2e-16 ***
## b 97.84378 3.83032 25.55 <2e-16 ***
## c 101.68624 5.56650 18.27 <2e-16 ***
## d 1.38333 0.04701 29.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5551 on 12520 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (318 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13052 7462.8
## 2 12738 6773.3 314 689.45 4.1293 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 146999.4
## 2 2 143248.7##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.95734 0.16586 5.772 8.02e-09 ***
## alpha 0.63553 0.01913 33.225 < 2e-16 ***
## A 211.21385 8.51246 24.812 < 2e-16 ***
## k 45.87774 1.81485 25.279 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7292 on 12738 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.86e-06
## (425 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12738 6773.3
## 2 12737 6293.4 1 479.9 971.25 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 143248.7
## 2 2a 142314.3
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.542e+00 1.891e-01 8.155 3.83e-16 ***
## alpha 8.373e-01 9.828e-03 85.188 < 2e-16 ***
## A 6.501e+02 1.211e+02 5.369 8.07e-08 ***
## k 3.806e+02 8.633e+01 4.408 1.05e-05 ***
## p 3.491e-02 5.787e-03 6.033 1.65e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7029 on 12737 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.192e-06
## (425 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13050 7396.2
## 2 12736 6127.9 314 1268.3 8.3946 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 142314.3
## 2 3 146886.4
## 3 4 141976.7##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.603e+00 1.888e-01 8.493 <2e-16 ***
## alpha 8.711e-01 8.328e-03 104.597 <2e-16 ***
## a 3.092e+01 1.000e+00 30.914 <2e-16 ***
## b 1.000e+02 4.613e+00 21.687 <2e-16 ***
## c 1.067e+02 7.018e+00 15.209 <2e-16 ***
## d 1.328e+00 5.460e-02 24.323 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6936 on 12736 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (425 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1339 479.03
## 2 1278 328.82 61 150.21 9.5706 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 15098.92
## 2 2 14148.58##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.43586 0.41265 1.056 0.291
## alpha 0.66378 0.05394 12.306 < 2e-16 ***
## A 515.74272 88.00272 5.861 5.86e-09 ***
## k 168.06395 32.33547 5.198 2.35e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5072 on 1278 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.019e-06
## (62 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1278 328.82
## 2 1277 328.80 1 0.019445 0.0755 0.7835
## model AIC
## 1 2 14148.58
## 2 2a 14150.50
## 3 2b 14150.16
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.43586 0.41265 1.056 0.291
## alpha 0.66378 0.05394 12.306 < 2e-16 ***
## A 515.74272 88.00272 5.861 5.86e-09 ***
## k 168.06395 32.33547 5.198 2.35e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5072 on 1278 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.019e-06
## (62 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1337 478.27
## 2 1276 328.64 61 149.63 9.524 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 14148.58
## 2 3 15100.79
## 3 4 14151.88##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.43586 0.41265 1.056 0.291
## alpha 0.66378 0.05394 12.306 < 2e-16 ***
## A 515.74272 88.00272 5.861 5.86e-09 ***
## k 168.06395 32.33547 5.198 2.35e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5072 on 1278 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.019e-06
## (62 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95765, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -12.034, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2284 617.34
## 2 1780 393.55 504 223.79 2.0084 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24037.04
## 2 2 18553.35##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.28799 0.28715 1.003 0.316
## alpha 0.72025 0.06709 10.736 <2e-16 ***
## A 258.89604 25.66614 10.087 <2e-16 ***
## k 100.18384 11.66369 8.589 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4702 on 1780 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.7e-06
## (506 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1780 393.55
## 2 1779 393.43 1 0.11381 0.5146 0.4732
## model AIC
## 1 2 18553.35
## 2 2a 18554.83
## 3 2b 18534.36
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.33240 0.29056 1.144 0.253
## alpha 0.73290 0.06789 10.796 <2e-16 ***
## A 147.26267 13.36288 11.020 <2e-16 ***
## k 38.77548 3.46207 11.200 <2e-16 ***
## s 1.70982 0.15327 11.155 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4676 on 1779 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 3.685e-06
## (506 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2282 595.32
## 2 1778 380.67 504 214.65 1.9892 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 18534.36
## 2 3 23957.97
## 3 4 18498.01##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.31661 0.28498 1.111 0.267
## alpha 0.72100 0.06578 10.961 < 2e-16 ***
## a 26.74983 3.84702 6.953 4.99e-12 ***
## b 93.30998 7.40246 12.605 < 2e-16 ***
## c 99.58965 6.91160 14.409 < 2e-16 ***
## d 1.09752 0.09364 11.720 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4627 on 1778 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (506 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96707, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.905, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 708 336.70
## 2 664 256.81 44 79.888 4.6944 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7311.058
## 2 2 6846.514##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.1773 0.4342 -0.408 0.683
## alpha 0.5661 0.0918 6.167 1.21e-09 ***
## A 194.5053 29.8795 6.510 1.49e-10 ***
## k 60.1946 10.3564 5.812 9.57e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6219 on 664 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.577e-06
## (46 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 664 256.81
## 2 663 253.78 1 3.0389 7.9392 0.004982 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6846.514
## 2 2a 6840.562
## 3 2b 6847.996
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.083028 0.451857 -0.184 0.85427
## alpha 0.578714 0.085314 6.783 2.60e-11 ***
## A 267.977416 86.436118 3.100 0.00202 **
## k 119.684829 58.411617 2.049 0.04086 *
## p 0.032739 0.008268 3.959 8.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6187 on 663 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.866e-06
## (46 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 706 321.06
## 2 662 239.34 44 81.727 5.1376 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 6840.562
## 2 3 7281.242
## 3 4 6803.432##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.18595 0.41602 -0.447 0.655
## alpha 0.64304 0.07575 8.489 < 2e-16 ***
## a 22.55850 2.84602 7.926 9.6e-15 ***
## b 75.97867 8.53695 8.900 < 2e-16 ***
## c 59.50943 5.44816 10.923 < 2e-16 ***
## d 0.99855 0.11429 8.737 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6013 on 662 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (46 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93732, p-value = 3.81e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.7344, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 155 28.883
## 2 151 26.739 4 2.1446 3.0278 0.01951 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1995.769
## 2 2 1953.364##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.08413 1.26662 -0.066 0.94713
## alpha 0.75308 0.24838 3.032 0.00286 **
## A 6807.62250 2948.62354 2.309 0.02231 *
## k 1327.87742 443.91819 2.991 0.00325 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4208 on 151 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 4.033e-06
## (4 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 151 26.739
## 2 150 25.778 1 0.96109 5.5926 0.01932 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 1953.364
## 2 2a 1949.690
## 3 2b NA
## 4 2c NA## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "263", , value =
## structure(list(: provided 32 variables to replace 31 variables##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.116e-02 1.317e+00 -0.008 0.99325
## alpha 8.636e-01 2.398e-01 3.601 0.00043 ***
## A 2.123e+04 2.453e+04 0.866 0.38806
## k 5.512e+03 6.778e+03 0.813 0.41741
## p 2.773e-03 2.618e-03 1.059 0.29123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4145 on 150 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.861e-06
## (4 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 153 30.979
## 2 149 28.736 4 2.2433 2.908 0.02364 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 1949.690
## 2 3 2010.835
## 3 4 1968.528##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.116e-02 1.317e+00 -0.008 0.99325
## alpha 8.636e-01 2.398e-01 3.601 0.00043 ***
## A 2.123e+04 2.453e+04 0.866 0.38806
## k 5.512e+03 6.778e+03 0.813 0.41741
## p 2.773e-03 2.618e-03 1.059 0.29123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4145 on 150 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.861e-06
## (4 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94849, p-value = 1.811e-05
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.165, p-value = 0.03038
## alternative hypothesis: two.sidedpredict and plot
plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 67.657
## 2 211 67.104 3 0.55338 0.58 0.6287
## model AIC
## 1 1 2322.942
## 2 2 2308.904##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.81309 0.95259 -0.854 0.3943
## alpha -0.08192 0.30561 -0.268 0.7889
## A 261.64141 103.82091 2.520 0.0125 *
## k 144.81331 58.56682 2.473 0.0142 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5639 on 211 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.783e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 211 67.104
## 2 210 67.101 1 0.0029778 0.0093 0.9232
## model AIC
## 1 2 2308.904
## 2 2a 2310.894
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.81309 0.95259 -0.854 0.3943
## alpha -0.08192 0.30561 -0.268 0.7889
## A 261.64141 103.82091 2.520 0.0125 *
## k 144.81331 58.56682 2.473 0.0142 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5639 on 211 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.783e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Error in nls(f_4, data = G_313, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: false convergence (8)
## model AIC
## 1 2 2308.904
## 2 3 2310.402
## 3 4 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.81309 0.95259 -0.854 0.3943
## alpha -0.08192 0.30561 -0.268 0.7889
## A 261.64141 103.82091 2.520 0.0125 *
## k 144.81331 58.56682 2.473 0.0142 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5639 on 211 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.783e-06
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91253, p-value = 6.107e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.3057, p-value = 0.1916
## alternative hypothesis: two.sidedpredict and plot
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
## Error in nls(f_1, data = G_322, start = c(tau = tau.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) :
## object 'nls_322.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 327 230.98
## 2 309 216.02 18 14.961 1.1889 0.2683
## model AIC
## 1 1 3395.864
## 2 2 3234.791##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5667 0.9405 -0.603 0.547218
## alpha 0.7128 0.1779 4.008 7.7e-05 ***
## A 78.9918 21.5520 3.665 0.000291 ***
## k 16.5318 5.5582 2.974 0.003168 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8361 on 309 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.565e-06
## (18 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 309 216.02
## 2 308 204.91 1 11.109 16.698 5.597e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 3234.791
## 2 2a 3220.267
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5777 0.4868 -3.241 0.00132 **
## alpha 0.8611 0.1216 7.079 9.87e-12 ***
## A 314.6391 431.8195 0.729 0.46678
## k 373.9015 734.0968 0.509 0.61088
## p 0.1303 0.1590 0.820 0.41313
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8157 on 308 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 4.316e-06
## (18 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Error in nls(f_4, data = G_331, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2a 3220.267
## 2 3 3396.105
## 3 4 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5777 0.4868 -3.241 0.00132 **
## alpha 0.8611 0.1216 7.079 9.87e-12 ***
## A 314.6391 431.8195 0.729 0.46678
## k 373.9015 734.0968 0.509 0.61088
## p 0.1303 0.1590 0.820 0.41313
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8157 on 308 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 4.316e-06
## (18 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88574, p-value = 1.515e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -7.0304, p-value = 2.059e-12
## alternative hypothesis: two.sidedpredict and plot
plotting 2
* Cannot fit model
332 - Great Plains Steppe
model selection 1
## Error in nls(f_1, data = G_332, start = c(tau = tau.start, A = A.start, :
## singular gradient
## model AIC
## 1 1 NA
## 2 2 2126.913##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7647 1.9348 0.395 0.69310
## alpha 0.8049 0.2993 2.689 0.00779 **
## A 386.0240 375.6275 1.028 0.30539
## k 267.8564 281.9470 0.950 0.34329
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8048 on 192 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.494e-06
## (36 observations deleted due to missingness)summary
- simple model: does not fit
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 2126.913
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7647 1.9348 0.395 0.69310
## alpha 0.8049 0.2993 2.689 0.00779 **
## A 386.0240 375.6275 1.028 0.30539
## k 267.8564 281.9470 0.950 0.34329
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8048 on 192 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.494e-06
## (36 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 225 139.58
## 2 190 115.51 35 24.075 1.1315 0.2946
## model AIC
## 1 2 2126.913
## 2 3 2445.978
## 3 4 2116.424##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.1813 2.1740 0.543 0.587502
## alpha 0.8182 0.2392 3.421 0.000763 ***
## a 25.7860 12.4200 2.076 0.039224 *
## b 77.3563 65.5343 1.180 0.239319
## c 143.4271 153.2697 0.936 0.350573
## d 1.0825 0.7444 1.454 0.147538
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7797 on 190 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (36 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88031, p-value = 2.28e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.9431, p-value = 7.689e-07
## alternative hypothesis: two.sidedpredict and plot
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6772 1333.1
## 2 6748 1126.2 24 206.94 51.665 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 71776.53
## 2 2 70468.36##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.80294 0.16480 4.872 1.13e-06 ***
## alpha 0.81438 0.02205 36.934 < 2e-16 ***
## A 397.95049 22.43035 17.742 < 2e-16 ***
## k 178.49005 10.18977 17.517 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4085 on 6748 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.987e-06
## (26 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6748 1126.2
## 2 6747 1121.6 1 4.5558 27.405 1.7e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 70468.36
## 2 2a 70442.99
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.718055 0.159681 4.497 7.01e-06 ***
## alpha 0.819495 0.022230 36.864 < 2e-16 ***
## A 318.006672 19.444264 16.355 < 2e-16 ***
## k 112.299842 11.187675 10.038 < 2e-16 ***
## p -0.034143 0.009135 -3.738 0.000187 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4077 on 6747 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.084e-06
## (26 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6770 1322.9
## 2 6746 1116.9 24 205.98 51.836 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 70442.99
## 2 3 71728.53
## 3 4 70416.75##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7253 0.1599 4.536 5.84e-06 ***
## alpha 0.8231 0.0219 37.579 < 2e-16 ***
## a 16.5607 2.7458 6.031 1.71e-09 ***
## b 150.2164 10.1830 14.752 < 2e-16 ***
## c 197.3137 23.5423 8.381 < 2e-16 ***
## d 1.6389 0.1071 15.297 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4069 on 6746 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (26 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8180 1388.9
## 2 8124 1275.5 56 113.39 12.897 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 90550.28
## 2 2 89408.34##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.76544 0.11795 6.49 9.11e-11 ***
## alpha 0.84668 0.03342 25.34 < 2e-16 ***
## A 256.52967 7.92961 32.35 < 2e-16 ***
## k 58.22137 2.29234 25.40 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3962 on 8124 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.65e-06
## (58 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8124 1275.5
## 2 8123 1275.5 1 0.000 0.0001 0.9932
## 3 8123 1268.7 0 0.000
## 4 8122 1236.9 1 31.815 208.9052 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 89408.34
## 2 2a 89410.33
## 3 2b 89367.31
## 4 2c 89162.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.93249 0.12409 7.515 6.31e-14 ***
## alpha 0.84839 0.03004 28.242 < 2e-16 ***
## A 158.69784 4.45097 35.655 < 2e-16 ***
## k 38.50195 0.80166 48.028 < 2e-16 ***
## p 0.25252 0.01316 19.195 < 2e-16 ***
## s 2.97626 0.17662 16.851 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3902 on 8122 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.741e-06
## (58 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8178 1358.7
## 2 8122 1234.5 56 124.24 14.597 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 89162.89
## 2 3 90374.77
## 3 4 89146.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.92767 0.12358 7.506 6.72e-14 ***
## alpha 0.84684 0.03017 28.068 < 2e-16 ***
## a 39.06110 1.95242 20.006 < 2e-16 ***
## b 113.70774 3.44940 32.965 < 2e-16 ***
## c 99.69266 2.70190 36.897 < 2e-16 ***
## d 1.16504 0.04168 27.949 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3899 on 8122 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (58 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
predict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 887 122.26
## 2 882 106.05 5 16.209 26.961 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9055.244
## 2 2 8902.357##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.01081 0.25502 -0.042 0.966
## alpha 0.89748 0.07232 12.410 < 2e-16 ***
## A 284.32641 32.44983 8.762 < 2e-16 ***
## k 91.18874 14.26526 6.392 2.64e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3468 on 882 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.12e-06
## (7 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 882 106.05
## 2 881 105.89 1 0.16567 1.3785 0.2407
## model AIC
## 1 2 8902.357
## 2 2a 8902.972
## 3 2b 8904.142
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.01081 0.25502 -0.042 0.966
## alpha 0.89748 0.07232 12.410 < 2e-16 ***
## A 284.32641 32.44983 8.762 < 2e-16 ***
## k 91.18874 14.26526 6.392 2.64e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3468 on 882 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.12e-06
## (7 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 885 121.92
## 2 880 105.92 5 16.008 26.6 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 8902.357
## 2 3 9056.791
## 3 4 8905.228##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.01081 0.25502 -0.042 0.966
## alpha 0.89748 0.07232 12.410 < 2e-16 ***
## A 284.32641 32.44983 8.762 < 2e-16 ***
## k 91.18874 14.26526 6.392 2.64e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3468 on 882 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.12e-06
## (7 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96279, p-value = 3.085e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -15.005, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1005 242.87
## 2 991 213.68 14 29.185 9.6678 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 10414.94
## 2 2 10205.89##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.69296 0.47940 1.445 0.149
## alpha 0.72680 0.06767 10.740 < 2e-16 ***
## A 222.81000 29.06880 7.665 4.26e-14 ***
## k 87.09494 11.66224 7.468 1.78e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4644 on 991 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.437e-06
## (14 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 991 213.68
## 2 990 212.16 1 1.52717 7.1264 0.00772 **
## 3 990 212.15 0 0.00000
## 4 989 212.13 1 0.01961 0.0914 0.76245
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 10205.89
## 2 2a 10200.76
## 3 2b 10200.72
## 4 2c 10202.63##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 5.958e-01 4.601e-01 1.295 0.196
## alpha 7.401e-01 6.343e-02 11.668 < 2e-16 ***
## A 6.172e+03 8.849e+04 0.070 0.944
## k 2.337e+04 5.044e+05 0.046 0.963
## s 7.039e-01 1.105e-01 6.369 2.9e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4629 on 990 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 7.767e-06
## (14 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Error in nls(f_4, data = G_M231, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 2b 10200.72
## 2 3 10415.55
## 3 4 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 5.958e-01 4.601e-01 1.295 0.196
## alpha 7.401e-01 6.343e-02 11.668 < 2e-16 ***
## A 6.172e+03 8.849e+04 0.070 0.944
## k 2.337e+04 5.044e+05 0.046 0.963
## s 7.039e-01 1.105e-01 6.369 2.9e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4629 on 990 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 7.767e-06
## (14 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96083, p-value = 1.104e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.338, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3298 2133.7
## 2 3224 1974.0 74 159.72 3.5251 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 43707.67
## 2 2 42724.57##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.34540 0.45370 -0.761 0.447
## alpha 1.04644 0.06748 15.508 < 2e-16 ***
## A 1189.96044 176.98435 6.724 2.09e-11 ***
## k 340.28730 31.51514 10.798 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7825 on 3224 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.189e-06
## (75 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3224 1974.0
## 2 3223 1944.4 1 29.586 49.041 3.038e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 42724.57
## 2 2a 42677.82
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.28026 0.46308 -0.605 0.545
## alpha 1.09425 0.06592 16.600 < 2e-16 ***
## A 885.21824 129.06241 6.859 8.29e-12 ***
## k 183.55735 21.87074 8.393 < 2e-16 ***
## p -0.05050 0.01100 -4.592 4.55e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7767 on 3223 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.082e-06
## (75 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3296 2088.0
## 2 3222 1937.6 74 150.37 3.3791 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 42677.82
## 2 3 43640.14
## 3 4 42668.50##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.27246 0.46316 -0.588 0.556
## alpha 1.08484 0.06781 15.997 < 2e-16 ***
## a 8.65719 10.66752 0.812 0.417
## b 568.18274 83.89943 6.772 1.50e-11 ***
## c 556.00691 107.65155 5.165 2.55e-07 ***
## d 2.03644 0.16919 12.037 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7755 on 3222 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (75 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94605, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -16.804, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1983 1184.8
## 2 1699 1053.3 284 131.5 0.7468 0.999
## model AIC
## 1 1 24895.19
## 2 2 21467.37##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.6101 0.2488 -6.472 1.26e-10 ***
## alpha 0.7419 0.1061 6.995 3.79e-12 ***
## A 760.7191 97.5974 7.794 1.12e-14 ***
## k 123.2836 16.8865 7.301 4.38e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7874 on 1699 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.299e-06
## (290 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1699 1053.3
## 2 1698 1053.2 1 0.07033 0.1134 0.7364
## 3 1698 1053.3 0 0.00000
## 4 1697 1052.9 1 0.44739 0.7211 0.3959
## model AIC
## 1 2 21467.37
## 2 2a 21469.26
## 3 2b 21469.36
## 4 2c 21470.64##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.6101 0.2488 -6.472 1.26e-10 ***
## alpha 0.7419 0.1061 6.995 3.79e-12 ***
## A 760.7191 97.5974 7.794 1.12e-14 ***
## k 123.2836 16.8865 7.301 4.38e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7874 on 1699 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.299e-06
## (290 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Error in nls(f_4, data = G_M261, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 2 21467.37
## 2 3 24897.19
## 3 4 NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.6101 0.2488 -6.472 1.26e-10 ***
## alpha 0.7419 0.1061 6.995 3.79e-12 ***
## A 760.7191 97.5974 7.794 1.12e-14 ***
## k 123.2836 16.8865 7.301 4.38e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7874 on 1699 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.299e-06
## (290 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89245, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.5593, p-value = 5.407e-11
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 363 122.71
## 2 361 118.29 2 4.4234 6.75 0.001324 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3833.912
## 2 2 3815.658##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.9278 0.3048 -6.326 7.46e-10 ***
## alpha 0.5586 0.1422 3.929 0.000102 ***
## A 570.5201 208.8668 2.732 0.006614 **
## k 230.4612 110.8456 2.079 0.038312 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5724 on 361 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 1.054e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 361 118.29
## 2 360 116.38 1 1.9039 5.8892 0.01572 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 3815.658
## 2 2a 3811.735
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.93341 0.29980 -6.449 3.63e-10 ***
## alpha 0.60955 0.13125 4.644 4.79e-06 ***
## A 1147.05673 1203.16291 0.953 0.341
## k 672.09791 853.57636 0.787 0.432
## p 0.02346 0.02058 1.140 0.255
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5686 on 360 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.202e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 361 120.72
## 2 359 114.30 2 6.413 10.071 5.553e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 3811.735
## 2 3 3831.912
## 3 4 3807.150## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "M313", , value =
## structure(list(: provided 32 variables to replace 31 variables##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.7796 0.3481 -5.112 5.19e-07 ***
## alpha 0.6348 0.1244 5.102 5.47e-07 ***
## a 46.4756 11.6701 3.982 8.26e-05 ***
## b 171.5834 39.2477 4.372 1.62e-05 ***
## c 174.5153 37.7519 4.623 5.29e-06 ***
## d 0.9408 0.1969 4.778 2.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5643 on 359 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94452, p-value = 1.864e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.87032, p-value = 0.3841
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1736 651.22
## 2 1714 586.85 22 64.369 8.5455 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18138.23
## 2 2 17803.52##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.79053 0.36102 -2.190 0.0287 *
## alpha 0.61269 0.04185 14.642 < 2e-16 ***
## A 251.44405 33.32753 7.545 7.32e-14 ***
## k 114.28468 11.51206 9.927 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5851 on 1714 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.744e-06
## (39 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'tau', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 + :
## variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1714 586.85
## 2 1713 580.51 1 6.3473 18.73 1.593e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 17803.52
## 2 2a 17786.84
## 3 2b 17796.89
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.764169 0.364512 -2.096 0.0362 *
## alpha 0.628230 0.040008 15.702 < 2e-16 ***
## A 322.311516 55.752829 5.781 8.80e-09 ***
## k 208.802587 46.686892 4.472 8.24e-06 ***
## p 0.044015 0.007603 5.789 8.39e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5821 on 1713 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.868e-06
## (39 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1734 645.18
## 2 1712 573.25 22 71.93 9.7645 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 17786.84
## 2 3 18126.02
## 3 4 17767.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.7928 0.3549 -2.234 0.0256 *
## alpha 0.6382 0.0391 16.325 < 2e-16 ***
## a 34.1072 4.7477 7.184 1.01e-12 ***
## b 124.4318 16.2354 7.664 2.99e-14 ***
## c 222.4559 27.7327 8.021 1.92e-15 ***
## d 1.3339 0.1216 10.974 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5787 on 1712 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (39 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92621, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.3972, p-value = 6.767e-08
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2617 1396.7
## 2 2521 1272.5 96 124.19 2.5628 3.378e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 28732.83
## 2 2 27767.83##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.26046 1.02586 1.229 0.219
## alpha 0.53094 0.05003 10.612 < 2e-16 ***
## A 151.66316 31.42990 4.825 1.48e-06 ***
## k 91.05449 7.89510 11.533 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7105 on 2521 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.095e-06
## (96 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2521 1272.5
## 2 2520 1238.5 1 34.045 69.273 < 2.2e-16 ***
## 3 2520 1255.3 0 0.000
## 4 2519 1213.2 1 42.165 87.549 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 27767.83
## 2 2a 27701.35
## 3 2b 27735.52
## 4 2c 27651.25##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.39322 1.06063 1.314 0.189
## alpha 0.63541 0.03940 16.126 < 2e-16 ***
## A 114.30325 24.72719 4.623 3.98e-06 ***
## k 79.86814 5.45346 14.645 < 2e-16 ***
## p 0.18745 0.01735 10.801 < 2e-16 ***
## s 2.42997 0.29534 8.228 3.02e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.694 on 2519 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 8.468e-06
## (96 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2615 1381.0
## 2 2519 1210.8 96 170.12 3.6866 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 27651.25
## 2 3 28707.13
## 3 4 27646.37##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.40226 1.06104 1.322 0.186
## alpha 0.63896 0.03895 16.403 < 2e-16 ***
## a 21.79948 4.55346 4.787 1.79e-06 ***
## b 83.33942 17.58868 4.738 2.28e-06 ***
## c 211.77444 20.64033 10.260 < 2e-16 ***
## d 1.25944 0.10074 12.502 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6933 on 2519 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (96 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89705, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.6568, p-value = 3.212e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1753 893.12
## 2 1693 800.14 60 92.977 3.2788 2.611e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 19820.05
## 2 2 19161.17##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.07826 1.90430 1.091 0.27527
## alpha 0.65732 0.05508 11.933 < 2e-16 ***
## A 239.10787 80.05515 2.987 0.00286 **
## k 164.44188 18.91300 8.695 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6875 on 1693 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.84e-06
## (61 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1693 800.14
## 2 1692 792.86 1 7.281 15.538 8.416e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 19161.17
## 2 2a 19147.66
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.271e+00 2.028e+00 1.120 0.26289
## alpha 6.701e-01 5.109e-02 13.117 < 2e-16 ***
## A 2.886e+02 1.054e+02 2.739 0.00623 **
## k 2.523e+02 5.970e+01 4.226 2.50e-05 ***
## p 1.837e-02 4.045e-03 4.542 5.97e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6845 on 1692 degrees of freedom
##
## Number of iterations to convergence: 35
## Achieved convergence tolerance: 9.399e-06
## (61 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1751 828.43
## 2 1691 714.93 60 113.5 4.4742 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 19147.66
## 2 3 19692.03
## 3 4 18974.09##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.57942 2.08937 1.235 0.21717
## alpha 0.70576 0.04116 17.147 < 2e-16 ***
## a 17.84902 5.91413 3.018 0.00258 **
## b 86.54624 28.63656 3.022 0.00255 **
## c 131.86513 5.63634 23.396 < 2e-16 ***
## d 0.95766 0.04899 19.548 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6502 on 1691 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (61 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93139, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.8623, p-value = 1.16e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 443 175.53
## 2 346 127.58 97 47.952 1.3407 0.02999 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4440.199
## 2 2 3467.793##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.53148 0.65254 -0.814 0.41594
## alpha 0.78101 0.09794 7.975 2.26e-14 ***
## A 127.24018 26.91846 4.727 3.32e-06 ***
## k 63.57045 21.02138 3.024 0.00268 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6072 on 346 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.418e-06
## (101 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 346 127.58
## 2 345 127.58 1 0.0007233 0.0020 0.9647
## 3 345 127.57 0 0.0000000
## 4 344 127.54 1 0.0283847 0.0766 0.7822
## model AIC
## 1 2 3467.793
## 2 2a 3469.791
## 3 2b 3469.768
## 4 2c 3471.690##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.53148 0.65254 -0.814 0.41594
## alpha 0.78101 0.09794 7.975 2.26e-14 ***
## A 127.24018 26.91846 4.727 3.32e-06 ***
## k 63.57045 21.02138 3.024 0.00268 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6072 on 346 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.418e-06
## (101 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 441 174.96
## 2 344 127.61 97 47.344 1.3157 0.03938 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 3467.793
## 2 3 4442.739
## 3 4 3471.887##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.53148 0.65254 -0.814 0.41594
## alpha 0.78101 0.09794 7.975 2.26e-14 ***
## A 127.24018 26.91846 4.727 3.32e-06 ***
## k 63.57045 21.02138 3.024 0.00268 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6072 on 346 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.418e-06
## (101 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9352, p-value = 3.254e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.1237, p-value = 9.143e-10
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 214 80.493
## 2 210 74.287 4 6.207 4.3866 0.001993 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 2156.928
## 2 2 2123.657##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.6002 0.5167 -3.097 0.002222 **
## alpha 0.5061 0.1376 3.678 0.000299 ***
## A 214.3813 55.2096 3.883 0.000138 ***
## k 87.8631 23.3697 3.760 0.000221 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5948 on 210 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.127e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 210 74.287
## 2 209 73.670 1 0.6167 1.7497 0.187365
## 3 209 74.208 0 0.0000
## 4 208 70.883 1 3.3245 9.7555 0.002043 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 2123.657
## 2 2a 2123.873
## 3 2b 2125.430
## 4 2c 2117.621##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.59170 0.50616 -3.145 0.00191 **
## alpha 0.55088 0.12860 4.284 2.81e-05 ***
## A 148.02788 37.19073 3.980 9.51e-05 ***
## k 66.06827 9.08317 7.274 7.00e-12 ***
## p 0.18027 0.03964 4.548 9.20e-06 ***
## s 3.03179 1.21785 2.489 0.01358 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5838 on 208 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 5.604e-06
## (6 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 76.519
## 2 208 70.029 4 6.4896 4.8188 0.0009756 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 2117.621
## 2 3 2149.940
## 3 4 2115.028##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.6230 0.4894 -3.316 0.001077 **
## alpha 0.5444 0.1286 4.234 3.45e-05 ***
## a 27.4152 7.3461 3.732 0.000245 ***
## b 116.7748 26.5422 4.400 1.73e-05 ***
## c 155.6772 22.0366 7.064 2.38e-11 ***
## d 1.0356 0.1981 5.228 4.16e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5802 on 208 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (6 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92949, p-value = 1.282e-08
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.81294, p-value = 0.4163
## alternative hypothesis: two.sidedpredict and plot
plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 2a | 4 | 4 |
| 212 | Laurentian Mixed Forest | 2a | 4 | 4 |
| 221 | Eastern Broadleaf Forest | 2 | 4 | 4 |
| 222 | Midwest Broadleaf Forest | 2b | 4 | 4 |
| 223 | Central Interior Broadleaf Forest | 2b | 4 | 4 |
| 231 | Southeastern Mixed Forest | 2c | 4 | 4 |
| 232 | Outer Coastal Plain Mixed Forest | 2a | 4 | 4 |
| 234 | Lower Mississippi Riverine Forest | 2 | 2 | 2 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 2b | 4 | 4 |
| 255 | Prairie Parkland (Subtropical) | 2a | 4 | 4 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 2a | 2a | 2a |
| 313 | Colorado Plateau Semi-Desert | 2 | 2 | 2 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | 2a | 2a | 2a |
| 332 | Great Plains Steppe | 2 | 4 | 4 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c | 4 | 4 |
| M223 | Ozark Broadleaf Forest Meadow | 2 | 2 | 2 |
| M231 | Ouachita Mixed Forest | 2b | 2b | 2b |
| M242 | Cascade Mixed Forest | 2a | 4 | 4 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 | 2 | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2c | 4 | 4 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a | 4 | 4 |
| M334 | Black Hills Coniferous Forest | 2 | 2 | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 2c | 4 | 4 |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6884 | 2879 | 0.8813228 | 0.0350003 | 0.5145805 | 1.2480652 | 0.8426533 | 0.0007099 | 0.7904238 | 0.8948828 | 439.3142 | 343.38465 | 535.2437 | 210.56313 | 1.424213e+02 | 2.787049e+02 | 37.964960 | 34.621151 | 41.30877 | 102.86051 | 93.75550 | 111.96552 | 114.69627 | 106.42936 | 122.9632 | 0.9253478 | 0.8481720 | 1.002524 |
| 212 | Laurentian Mixed Forest | east | 22685 | 9493 | 0.5000581 | 0.0134207 | 0.2729862 | 0.7271300 | 0.7837680 | 0.0002184 | 0.7547983 | 0.8127376 | 224.9575 | 204.62713 | 245.2879 | 120.74409 | 1.040583e+02 | 1.374299e+02 | 23.589205 | 22.253731 | 24.92468 | 78.95623 | 74.83541 | 83.07706 | 109.35069 | 103.55458 | 115.1468 | 1.1945977 | 1.1375776 | 1.251618 |
| 221 | Eastern Broadleaf Forest | east | 7307 | 3560 | 0.1820966 | 0.0137947 | -0.0481413 | 0.4123346 | 0.8234621 | 0.0006286 | 0.7743142 | 0.8726099 | 489.3046 | 439.62656 | 538.9827 | 148.21326 | 1.309803e+02 | 1.654463e+02 | 30.305398 | 26.289091 | 34.32170 | 165.27194 | 150.60803 | 179.93586 | 136.54936 | 118.54243 | 154.5563 | 1.3442406 | 1.2204710 | 1.468010 |
| 222 | Midwest Broadleaf Forest | east | 5846 | 2589 | 0.2191055 | 0.0393389 | -0.1697320 | 0.6079429 | 0.8609837 | 0.0012194 | 0.7925247 | 0.9294428 | 245.8923 | 196.84307 | 294.9415 | 74.26959 | 5.397287e+01 | 9.456632e+01 | 25.857990 | 22.792685 | 28.92330 | 113.29766 | 102.37876 | 124.21657 | 102.72706 | 93.94705 | 111.5071 | 1.0226878 | 0.9327978 | 1.112578 |
| 223 | Central Interior Broadleaf Forest | east | 10006 | 3860 | 0.1196573 | 0.0101686 | -0.0780119 | 0.3173264 | 0.7696806 | 0.0006788 | 0.7186077 | 0.8207536 | 180.0212 | 164.11187 | 195.9306 | 39.98216 | 3.502045e+01 | 4.494387e+01 | 31.403445 | 27.604600 | 35.20229 | 103.16970 | 96.41229 | 109.92712 | 102.24785 | 94.39348 | 110.1022 | 1.2127067 | 1.1106876 | 1.314726 |
| 231 | Southeastern Mixed Forest | east | 12844 | 5935 | 2.1217238 | 0.0335259 | 1.7628180 | 2.4806297 | 0.8066003 | 0.0001042 | 0.7865912 | 0.8266093 | 127.7848 | 118.88207 | 136.6876 | 32.08778 | 3.037208e+01 | 3.380348e+01 | 26.098748 | 24.594334 | 27.60316 | 97.84378 | 90.33575 | 105.35180 | 101.68624 | 90.77504 | 112.5974 | 1.3833283 | 1.2911888 | 1.475468 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13167 | 6463 | 1.6031145 | 0.0356297 | 1.2331199 | 1.9731092 | 0.8710963 | 0.0000694 | 0.8547719 | 0.8874207 | 650.0955 | 412.74063 | 887.4504 | 380.55124 | 2.113342e+02 | 5.497683e+02 | 30.917153 | 28.956773 | 32.87753 | 100.04223 | 91.00020 | 109.08425 | 106.73662 | 92.98075 | 120.4925 | 1.3280105 | 1.2209872 | 1.435034 |
| 234 | Lower Mississippi Riverine Forest | east | 1344 | 759 | 0.4358633 | 0.1702808 | -0.3736843 | 1.2454108 | 0.6637788 | 0.0029096 | 0.5579571 | 0.7696004 | 515.7427 | 343.09704 | 688.3884 | 168.06395 | 1.046275e+02 | 2.315004e+02 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | pacific | 85 | 85 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2290 | 903 | 0.3166111 | 0.0812149 | -0.2423245 | 0.8755466 | 0.7210025 | 0.0043272 | 0.5919852 | 0.8500198 | 147.2627 | 121.05407 | 173.4713 | 38.77548 | 3.198534e+01 | 4.556563e+01 | 26.749834 | 19.204673 | 34.29499 | 93.30998 | 78.79153 | 107.82843 | 99.58965 | 86.03393 | 113.1454 | 1.0975160 | 0.9138552 | 1.281177 |
| 255 | Prairie Parkland (Subtropical) | east | 714 | 318 | -0.1859510 | 0.1730759 | -1.0028363 | 0.6309342 | 0.6430371 | 0.0057374 | 0.4943060 | 0.7917682 | 267.9774 | 98.25591 | 437.6989 | 119.68483 | 4.990785e+00 | 2.343789e+02 | 22.558497 | 16.970193 | 28.14680 | 75.97867 | 59.21591 | 92.74144 | 59.50943 | 48.81167 | 70.2072 | 0.9985515 | 0.7741415 | 1.222962 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 26 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 159 | 157 | -0.0111604 | 1.7339910 | -2.6130542 | 2.5907333 | 0.8636392 | 0.0575211 | 0.3897468 | 1.3375316 | 21233.8336 | -27233.49640 | 69701.1637 | 5511.67996 | -7.881182e+03 | 1.890454e+04 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | -0.8130865 | 0.9074242 | -2.6908955 | 1.0647226 | -0.0819227 | 0.0933971 | -0.6843616 | 0.5205163 | 261.6414 | 56.98230 | 466.3005 | 144.81331 | 2.936225e+01 | 2.602644e+02 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | -1.5776899 | 0.2369940 | -2.5356043 | -0.6197756 | 0.8611181 | 0.0147981 | 0.6217530 | 1.1004832 | 314.6391 | -535.05048 | 1164.3287 | 373.90147 | -1.070578e+03 | 1.818381e+03 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | 1.1813235 | 4.7263191 | -3.1069723 | 5.4696194 | 0.8182341 | 0.0572011 | 0.3464693 | 1.2899989 | 386.0240 | -354.86226 | 1126.9103 | 267.85640 | -2.882549e+02 | 8.239677e+02 | 25.785961 | 1.287256 | 50.28467 | 77.35625 | -51.91195 | 206.62445 | 143.42713 | -158.90159 | 445.7559 | 1.0825214 | -0.3858405 | 2.550883 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6778 | 3008 | 0.7253080 | 0.0255701 | 0.4118408 | 1.0387753 | 0.8230698 | 0.0004797 | 0.7801339 | 0.8660057 | 318.0067 | 279.88978 | 356.1236 | 112.29984 | 9.036847e+01 | 1.342312e+02 | 16.560727 | 11.178056 | 21.94340 | 150.21644 | 130.25461 | 170.17827 | 197.31368 | 151.16330 | 243.4641 | 1.6388804 | 1.4288507 | 1.848910 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8186 | 3765 | 0.9276701 | 0.0152730 | 0.6854135 | 1.1699266 | 0.8468373 | 0.0009103 | 0.7876954 | 0.9059793 | 158.6978 | 149.97279 | 167.4229 | 38.50195 | 3.693050e+01 | 4.007340e+01 | 39.061096 | 35.233846 | 42.88835 | 113.70774 | 106.94603 | 120.46944 | 99.69266 | 94.39625 | 104.9891 | 1.1650416 | 1.0833293 | 1.246754 |
| M223 | Ozark Broadleaf Forest Meadow | east | 893 | 348 | -0.0108055 | 0.0650335 | -0.5113158 | 0.4897048 | 0.8974822 | 0.0052297 | 0.7555490 | 1.0394153 | 284.3264 | 220.63852 | 348.0143 | 91.18874 | 6.319092e+01 | 1.191866e+02 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 1009 | 496 | 0.5958020 | 0.2116527 | -0.3069975 | 1.4986015 | 0.7400715 | 0.0040231 | 0.6156024 | 0.8645405 | 6171.9126 | -167471.37461 | 179815.1997 | 23371.75341 | -9.664988e+05 | 1.013242e+06 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 3303 | 3286 | -0.2724568 | 0.2145181 | -1.1805767 | 0.6356631 | 1.0848443 | 0.0045988 | 0.9518801 | 1.2178085 | 885.2182 | 632.16552 | 1138.2710 | 183.55735 | 1.406754e+02 | 2.264393e+02 | 8.657191 | -12.258617 | 29.57300 | 568.18274 | 403.68107 | 732.68440 | 556.00691 | 344.93446 | 767.0793 | 2.0364416 | 1.7047151 | 2.368168 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1993 | 1828 | -1.6100870 | 0.0618959 | -2.0980518 | -1.1221222 | 0.7419469 | 0.0112490 | 0.5339226 | 0.9499712 | 760.7191 | 569.29536 | 952.1428 | 123.28357 | 9.016312e+01 | 1.564040e+02 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -1.7795966 | 0.1328687 | -2.4641675 | -1.0950257 | 0.6095510 | 0.0154818 | 0.3514346 | 0.8676674 | 1147.0567 | -1219.05393 | 3513.1674 | 672.09791 | -1.006524e+03 | 2.350720e+03 | 46.475597 | 23.525317 | 69.42588 | 171.58342 | 94.39917 | 248.76766 | 174.51526 | 100.27252 | 248.7580 | 0.9407765 | 0.5535532 | 1.328000 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1757 | 1757 | -0.7928071 | 0.1259838 | -1.4889727 | -0.0966416 | 0.6382489 | 0.0015285 | 0.5615682 | 0.7149295 | 322.3115 | 212.96072 | 431.6623 | 208.80259 | 1.172333e+02 | 3.003719e+02 | 34.107158 | 24.795199 | 43.41912 | 124.43177 | 92.58849 | 156.27504 | 222.45594 | 168.06240 | 276.8495 | 1.3338961 | 1.0955011 | 1.572291 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2621 | 2611 | 1.4022553 | 1.1258016 | -0.6783407 | 3.4828512 | 0.6389574 | 0.0015174 | 0.5625721 | 0.7153427 | 114.3033 | 65.81555 | 162.7910 | 79.86814 | 6.917442e+01 | 9.056187e+01 | 21.799478 | 12.870561 | 30.72840 | 83.33942 | 48.84966 | 117.82918 | 211.77444 | 171.30069 | 252.2482 | 1.2594430 | 1.0618959 | 1.456990 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1758 | 1747 | 2.5794211 | 4.3654790 | -1.5186077 | 6.6774498 | 0.7057566 | 0.0016941 | 0.6250269 | 0.7864864 | 288.5627 | 81.92180 | 495.2036 | 252.32934 | 1.352299e+02 | 3.694287e+02 | 17.849018 | 6.249232 | 29.44880 | 86.54624 | 30.37942 | 142.71306 | 131.86513 | 120.81018 | 142.9201 | 0.9576648 | 0.8615742 | 1.053755 |
| M334 | Black Hills Coniferous Forest | interior west | 451 | 179 | -0.5314777 | 0.4258135 | -1.8149296 | 0.7519741 | 0.7810081 | 0.0095919 | 0.5883792 | 0.9736371 | 127.2402 | 74.29577 | 180.1846 | 63.57045 | 2.222468e+01 | 1.049162e+02 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | -1.6230333 | 0.2395404 | -2.5879099 | -0.6581567 | 0.5443555 | 0.0165315 | 0.2908785 | 0.7978326 | 148.0279 | 74.70880 | 221.3470 | 66.06827 | 4.816139e+01 | 8.397515e+01 | 27.415227 | 12.932883 | 41.89757 | 116.77484 | 64.44866 | 169.10102 | 155.67721 | 112.23356 | 199.1209 | 1.0355782 | 0.6450688 | 1.426087 |
parameter variance co-variance
## tau alpha a b c
## tau 0.035000316 -2.921063e-05 -0.221947693 -0.728760036 -0.065744162
## alpha -0.005860223 7.098746e-04 0.003592054 0.003559913 -0.001916846
## a -0.695502026 7.903798e-02 2.909594753 2.744898036 -1.762387722
## b -0.838674289 2.876692e-02 0.346461298 21.572996391 10.188445675
## c -0.083330341 -1.705998e-02 -0.245000603 0.520157238 17.784272555
## d -0.098859549 -3.553039e-03 -0.427336934 0.491775292 0.890143172
## d
## tau -7.281331e-04
## alpha -3.726893e-06
## a -2.869742e-02
## b 8.992451e-02
## c 1.477863e-01
## d 1.549931e-03## tau alpha a b c
## tau 0.01342069 3.715109e-05 -0.059874535 -0.214085327 -0.039346856
## alpha 0.02169785 2.184414e-04 0.001849154 -0.001227538 -0.003731858
## a -0.75856901 1.836310e-01 0.464214943 0.744225598 -0.251206642
## b -0.87900550 -3.950571e-02 0.519561823 4.419932394 2.866276922
## c -0.11485816 -8.538801e-02 -0.124684042 0.461051720 8.744225998
## d -0.07833891 -1.326805e-01 -0.327705899 0.356059946 0.861404142
## d
## tau -2.640082e-04
## alpha -5.704624e-05
## a -6.495256e-03
## b 2.177627e-02
## c 7.410033e-02
## d 8.462622e-04## tau alpha a b c
## tau 0.01379470 0.0001070956 -0.081089361 -0.57196291 -0.12409957
## alpha 0.03636903 0.0006285900 0.004111461 -0.00807586 -0.01450298
## a -0.33697803 0.0800398611 4.197708988 -3.98500970 -9.12838149
## b -0.65100249 -0.0430601920 -0.260012446 55.95748230 54.49519969
## c -0.11502572 -0.0629729919 -0.485029853 0.79306725 84.37976186
## d -0.06814007 -0.0540858244 -0.686476644 0.72968273 0.93876072
## d
## tau -5.053030e-04
## alpha -8.561706e-05
## a -8.880248e-02
## b 3.446326e-01
## c 5.444616e-01
## d 3.986450e-03## tau alpha a b c
## tau 0.03933893 0.0002002966 -0.209573026 -0.957531457 -0.066097376
## alpha 0.02891933 0.0012194057 0.004329288 0.002418565 -0.009474419
## a -0.67578279 0.0792912841 2.444747096 3.480176571 -1.611864305
## b -0.86680125 0.0124354458 0.399633672 31.020191294 11.440378332
## c -0.07441064 -0.0605815744 -0.230183181 0.458648766 20.057455806
## d -0.02685154 -0.0550250884 -0.440098893 0.354442689 0.891087602
## d
## tau -2.441938e-04
## alpha -8.810269e-05
## a -3.155161e-02
## b 9.051542e-02
## c 1.829838e-01
## d 2.102367e-03## tau alpha a b c
## tau 0.01016860 0.0002502204 -0.060270912 -0.236544481 -0.032910530
## alpha 0.09523783 0.0006788366 0.002643107 -0.003074269 -0.003138704
## a -0.30841404 0.0523466584 3.755659414 -2.437359318 -3.026636229
## b -0.68047144 -0.0342284235 -0.364841361 11.883511259 8.561117664
## c -0.08145199 -0.0300652689 -0.389775457 0.619805518 16.054813787
## d -0.02256004 -0.0390210645 -0.709844532 0.632382542 0.862921495
## d
## tau -1.183977e-04
## alpha -5.291208e-05
## a -7.159446e-02
## b 1.134554e-01
## c 1.799480e-01
## d 2.708608e-03## tau alpha a b c
## tau 0.03352594 0.0002965874 -0.098777600 -0.565450193 -0.13963326
## alpha 0.15868128 0.0001042012 0.001675951 -0.008883086 -0.01084275
## a -0.70289589 0.2139182457 0.589052502 1.077571822 -0.90164254
## b -0.80624756 -0.2271914222 0.366550437 14.671379950 13.77622997
## c -0.13699859 -0.1908186409 -0.211045001 0.646119105 30.98593731
## d -0.17654887 -0.2766022134 -0.324659485 0.612185150 0.92770625
## d
## tau -0.0015195358
## alpha -0.0001327234
## a -0.0117127976
## b 0.1102234025
## c 0.2427439102
## d 0.0022095869## tau alpha a b c
## tau 0.03562969 1.651537e-04 -0.148899675 -0.660064569 -0.111932405
## alpha 0.10505922 6.935795e-05 0.001501598 -0.006670866 -0.009278125
## a -0.78874516 1.802829e-01 1.000234882 1.995880936 -1.217817267
## b -0.75806052 -1.736431e-01 0.432620538 21.279087381 21.081493440
## c -0.08449887 -1.587498e-01 -0.173513082 0.651217360 49.249044597
## d -0.10994254 -2.337003e-01 -0.272208128 0.586348347 0.927165488
## d
## tau -0.0011330800
## alpha -0.0001062664
## a -0.0148641766
## b 0.1476797587
## c 0.3552588718
## d 0.0029811068## tau alpha A k
## tau 0.170280754 0.0008129697 -18.9614855 0.06854134
## alpha 0.036523847 0.0029095786 -0.3496619 -0.18957883
## A -0.522147814 -0.0736609156 7744.4793212 2405.81801427
## k 0.005136775 -0.1086914910 0.8454490 1045.58292504## tau alpha a b c
## tau 0.08121491 0.002029994 -0.394868460 -1.63497670 -0.17410264
## alpha 0.10828611 0.004327212 0.002434364 -0.01279668 -0.01152039
## a -0.36017195 0.009619593 14.799579243 -5.51284674 -8.87541025
## b -0.77502804 -0.026279487 -0.193586448 54.79646823 26.57701308
## c -0.08839112 -0.025338687 -0.333798894 0.51945870 47.77027228
## d -0.04454636 -0.008196097 -0.691606270 0.53724831 0.83196932
## d
## tau -0.0011887835
## alpha -0.0000504875
## a -0.2491473482
## b 0.3724122932
## c 0.5384666779
## d 0.0087689042## tau alpha a b c d
## tau 0.17307586 0.005425805 -0.74851944 -3.22751522 -0.11247870 -0.004053604
## alpha 0.17218171 0.005737437 0.02376493 -0.07485858 -0.03241448 -0.001294910
## a -0.63219000 0.110240301 8.09980265 10.19081895 -3.11422960 -0.137701193
## b -0.90875608 -0.115765707 0.41943932 72.87951105 10.45617802 0.218224532
## c -0.04962515 -0.078547042 -0.20084600 0.22481228 29.68249676 0.510187051
## d -0.08525575 -0.149582693 -0.42335149 0.22366676 0.81936956 0.013061672## tau alpha A k p
## tau 1.73399103 0.02574439 -6.375772e+03 8.260465e+02 -3.628483e-04
## alpha 0.08151651 0.05752111 5.321152e+02 1.767955e+02 -3.727927e-05
## A -0.19739056 0.09045011 6.016805e+08 1.589468e+08 -5.821608e+01
## k 0.09254944 0.10875528 9.560082e-01 4.594249e+07 -1.658691e+01
## p -0.10524743 -0.05936953 -9.065042e-01 -9.346908e-01 6.854572e-06## tau alpha A k
## tau 0.907424207 0.005189997 -79.0522667 -0.3329832
## alpha 0.017827693 0.093397146 1.4336847 -0.3263735
## A -0.799326696 0.045185804 10778.7812606 3608.3755944
## k -0.005968503 -0.018234608 0.5934378 3430.0727759## tau alpha A k p
## tau 0.23699401 -0.002182051 -8.560042e+01 -1.030075e+02 2.051283e-02
## alpha -0.03684627 0.014798085 3.791168e+00 6.785294e+00 -7.791469e-04
## A -0.40719732 0.072171874 1.864681e+05 3.133164e+05 -6.735300e+01
## k -0.28823494 0.075982322 9.883881e-01 5.388981e+05 -1.143665e+02
## p 0.26508716 -0.040294750 -9.812654e-01 -9.801155e-01 2.526599e-02## tau alpha a b c
## tau 4.72631913 0.05249845 -23.05980787 -68.9207833 -7.0927740
## alpha 0.10096774 0.05720114 -0.01641209 -1.1085700 -2.1816517
## a -0.85403218 -0.00552512 154.25521616 142.8292819 -486.0487750
## b -0.48374914 -0.07072815 0.17548049 4294.7408443 8665.4727248
## c -0.02128621 -0.05951506 -0.25533111 0.8627155 23491.5891406
## d 0.01871121 -0.06713620 -0.35261164 0.7972728 0.9732278
## d
## tau 0.03028121
## alpha -0.01195278
## a -3.26006651
## b 38.89424115
## c 111.04029305
## d 0.55414033## tau alpha a b c
## tau 0.025570091 -1.973382e-05 -0.052365829 -0.834029379 -0.10026445
## alpha -0.005634433 4.797222e-04 0.003555771 -0.004613703 -0.02926528
## a -0.119264181 5.912445e-02 7.539519024 -16.636614000 -45.50200113
## b -0.512201496 -2.068618e-02 -0.595002439 103.692834678 205.39796269
## c -0.026633705 -5.675558e-02 -0.703897505 0.856786289 554.24080940
## d -0.029817572 -5.060586e-02 -0.861469451 0.832870121 0.95576069
## d
## tau -0.0005108497
## alpha -0.0001187546
## a -0.2534349045
## b 0.9086704009
## c 2.4107553457
## d 0.0114791426## tau alpha a b c
## tau 0.01527304 0.0002214056 -0.100681725 -0.34445406 -0.045997595
## alpha 0.05938036 0.0009102617 0.004027365 -0.00290831 -0.003636241
## a -0.41726690 0.0683697334 3.811957174 -0.84697948 -1.388952990
## b -0.80802604 -0.0279456557 -0.125763796 11.89834312 4.219214015
## c -0.13775367 -0.0446067129 -0.263296020 0.45270893 7.300262789
## d -0.06993240 -0.0444134044 -0.649613306 0.49882427 0.787787492
## d
## tau -3.602595e-04
## alpha -5.585622e-05
## a -5.286926e-02
## b 7.172410e-02
## c 8.872635e-02
## d 1.737595e-03## tau alpha A k
## tau 0.06503351 0.0003149599 -4.84939308 -0.274028401
## alpha 0.01707841 0.0052297213 0.08019419 -0.008950672
## A -0.58601184 0.0341736404 1052.99139925 390.856209155
## k -0.07532640 -0.0086763402 0.84435451 203.497724085## tau alpha A k s
## tau 0.21165272 -0.000426117 -3.925350e+03 -2.081147e+04 4.396630e-03
## alpha -0.01460276 0.004023131 4.118944e+02 2.391752e+03 -7.786722e-04
## A -0.09642461 0.073388019 7.829919e+09 4.463185e+10 -9.517529e+03
## k -0.08967919 0.074754103 9.999244e-01 2.544475e+11 -5.438507e+04
## s 0.08647337 -0.111082845 -9.732401e-01 -9.755625e-01 1.221381e-02## tau alpha a b c
## tau 0.214518069 -0.0003550751 -0.538082292 -34.0507812 -1.713471e-01
## alpha -0.011304849 0.0045988268 -0.001952738 0.2165018 -9.010198e-02
## a -0.108906395 -0.0026993365 113.795938370 -187.2173158 -7.914804e+02
## b -0.876266309 0.0380521208 -0.209181661 7039.1149112 4.143780e+03
## c -0.003436565 -0.0123421416 -0.689217871 0.4587936 1.158886e+04
## d 0.004287326 -0.0026532337 -0.865182793 0.4050849 9.433785e-01
## d
## tau 3.359598e-04
## alpha -3.044163e-05
## a -1.561493e+00
## b 5.750080e+00
## c 1.718206e+01
## d 2.862449e-02## tau alpha A k
## tau 0.06189590 0.000749934 -19.3766256 0.06735537
## alpha 0.02842076 0.011248975 0.4502756 -0.02288591
## A -0.79801136 0.043499450 9525.2479320 939.29423390
## k 0.01603255 -0.012778299 0.5699344 285.15256354## tau alpha a b c
## tau 0.12117346 0.0004659518 -2.869971606 -10.5598574 -1.4162456
## alpha 0.01075787 0.0154818231 0.211107563 0.2375863 0.2476308
## a -0.70648113 0.1453849539 136.190419918 182.2894711 -0.7594473
## b -0.77293034 0.0486515078 0.397992013 1540.3800963 911.1858983
## c -0.10776941 0.0527174423 -0.001723793 0.6149697 1425.2090609
## d -0.09311381 0.0212221632 -0.159757755 0.5087182 0.9108688
## d
## tau -0.0063821151
## alpha 0.0005199331
## a -0.3670980089
## b 3.9313166965
## c 6.7708302340
## d 0.0387698037## tau alpha a b c
## tau 0.125983768 -0.0003188892 -1.41689490 -5.18807203 0.01574039
## alpha -0.022980088 0.0015284863 0.03441449 0.01682163 -0.04159551
## a -0.840803518 0.1854064100 22.54092022 49.56743350 -28.24525413
## b -0.900297860 0.0265017652 0.64305501 263.58759388 168.71913858
## c 0.001599065 -0.0383639752 -0.21451989 0.37472250 769.10244390
## d 0.007372106 -0.0733255715 -0.34398193 0.31617058 0.90706181
## d
## tau 0.0003180466
## alpha -0.0003484401
## a -0.1985013128
## b 0.6239156455
## c 3.0575313187
## d 0.0147735161## tau alpha a b c
## tau 1.12580162 0.001287381 -4.69961198 -18.22958907 -1.51948038
## alpha 0.03114749 0.001517421 0.01319642 -0.02110376 -0.07847249
## a -0.97272280 0.074398008 20.73404032 74.91340638 -1.13982524
## b -0.97681561 -0.030801621 0.93537169 309.36181647 84.94681404
## c -0.06938212 -0.097599543 -0.01212773 0.23398990 426.02319075
## d -0.04144872 -0.172378031 -0.08748768 0.15390967 0.88230682
## d
## tau -0.0044305334
## alpha -0.0006764705
## a -0.0401331102
## b 0.2727176141
## c 1.8346371713
## d 0.0101491076## tau alpha a b c
## tau 4.3654790031 0.001714325 -12.22044683 -59.60602527 0.011697419
## alpha 0.0199343769 0.001694139 0.01017155 -0.01455555 -0.009423365
## a -0.9889633540 0.041785148 34.97694466 166.48781145 -0.782545650
## b -0.9962157974 -0.012349045 0.98303894 820.05234162 5.557432082
## c 0.0009932912 -0.040619450 -0.02347584 0.03443149 31.768378767
## d -0.0141162175 -0.146668035 -0.05483698 0.01995116 0.740111498
## d
## tau -0.0014449615
## alpha -0.0002957549
## a -0.0158886299
## b 0.0279905154
## c 0.2043697693
## d 0.0024001808## tau alpha A k
## tau 0.42581347 0.002555004 -12.70544736 0.9144590
## alpha 0.03997885 0.009591872 -0.09230591 -0.1661125
## A -0.72331934 -0.035012862 724.60340793 351.9518421
## k 0.06666431 -0.080684364 0.62197351 441.8983042## tau alpha a b c d
## tau 0.23954039 -0.01240639 -3.06757093 -12.13769640 -0.6793393 0.005296252
## alpha -0.19715142 0.01653151 0.30052853 0.88825621 0.1615168 0.001218204
## a -0.85319590 0.31818008 53.96509503 146.67611491 -2.6986202 -0.326810904
## b -0.93435139 0.26028272 0.75225706 704.48752743 124.6222444 -0.100127663
## c -0.06298735 0.05700561 -0.01667022 0.21306639 485.6103600 3.267978853
## d 0.05462987 0.04783156 -0.22459030 -0.01904445 0.7486627 0.039237213## png
## 2## png
## 2plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
plot alpha (biomass compensation effect)
plot A (asymptote of B)
## Warning: Removed 12 rows containing missing values (`geom_point()`).
plot k (stand age at half biomass asymptote)
## Warning: Removed 12 rows containing missing values (`geom_point()`).
Caclulations - weighted averages
tau (productivity trend – in % / year – 2000-2021)
## region weighted.ge weighted.tau.std_Error 95 % CI, upper
## 1 entire US 0.69247579 0.09453550 0.8777654
## 2 pacific -0.06675040 0.02784261 -0.0121789
## 3 east 0.66813069 0.04057178 0.7476514
## 4 interior west 0.09109551 0.08071977 0.2493063
## 95 % CI, lower
## 1 0.50718621
## 2 -0.12132191
## 3 0.58860999
## 4 -0.06711524alpha (biomass compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.79932769 1.356089e-07 0.79932796
## 2 pacific 0.08789315 5.175654e-03 0.09803743
## 3 east 0.62778715 5.008890e-03 0.63760458
## 4 interior west 0.08364739 2.998747e-03 0.08952494
## 95 % CI, lower
## 1 0.79932743
## 2 0.07774887
## 3 0.61796973
## 4 0.07776985A (asymptote of forest biomass in Mg/ha)
## region weighted.A
## 1 entire US 459.2681
## 2 pacific 1418.2708
## 3 east 377.0926
## 4 interior west 0.0000K (stand age at half maturation in years)
## region weighted.k
## 1 entire US 360.2866
## 2 pacific 314.7279
## 3 east 395.6918
## 4 interior west 188.0424Model Bookeeping
1. Empirical Delta-B total
2. Delta-B due to Delta-STDAGE
3. Delta-B due to Delta-Year (ge)
Delta B constants
FUNCTION: simulate f(age) – accounting for uncertainty in the age function – rmvnorm
solve for f(age)
5. Delta B due to B_l
BK_df
Delta B
## Warning: Removed 12044 rows containing missing values (`geom_point()`).
## Warning: Removed 12044 rows containing missing values (`geom_point()`).
## Warning: Removed 6022 rows containing missing values (`geom_point()`).
## Warning: Removed 12044 rows containing missing values (`geom_point()`).
## Warning: Removed 32294 rows containing missing values (`geom_point()`).
Stand age densities
## Warning: package 'ggridges' was built under R version 4.2.2## Picking joint bandwidth of 4.71## Picking joint bandwidth of 9.91## Picking joint bandwidth of 11.6## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.
Delta B age vs. Delta Stand age
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 32294 rows containing missing values (`geom_point()`).## Picking joint bandwidth of 4.71## Picking joint bandwidth of 9.91## Picking joint bandwidth of 11.6## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).
## Warning: Removed 12044 rows containing missing values (`geom_point()`).## Picking joint bandwidth of 4.71## Picking joint bandwidth of 9.91## Picking joint bandwidth of 11.6## Warning: Removed 90 rows containing non-finite values (`stat_density_ridges()`).## png
## 2```